Arch Failure in Sandstone in the Case of Nonlinear Flow

A mathematical model of elastic--plastic deformations and stability of sand in a compacted zone around a perforation with a nonlinear flow is developed for a gas well. Laser processing of porous materials is accompanied by similar problems too. The stresses in porous material and the effect of flowing fluids have been analyzed theoretically. The criteria describing stability of sand arches are given. Critical rates of production are found that do not result in destruction of the reservoir near the perforation opening by tensile and shear stresses. The influence of variable permeability on the stability of the arches around the perforations has been studied. The significant influence of water on elastic–plastic deformation and destruction of sand arches is shown within the approach of constant saturation. The results are obtained for both fluid production from the well and gas injection into the reservoir. The conditions of arch stability near the perforated opening are always fulfilled with fluid injection.     

Understanding STEM‐focused elementary schools: Case study of Walter Bracken STEAM Academy

Increasingly, STEM focused high schools are used prepare students for college STEM majors and launch them into STEM careers. Yet a new focus on STEM education at the elementary levels suggests that the importance of STEM education is much broader than a preparation for workforce needs in high school or college. This paper describes a case study designed to articulate the mission and design of an effective and nationally recognized STEM‐focused elementary school. As described through the six most impactful components of STEM‐focused elementary school design at Walter Bracken STEAM Academy, the case study emphasizes the school's strong and inclusive school leadership, with staff organized into grade level groups empowered to innovate and honing their teaching practices. External partnerships are leveraged to broaden student learning opportunities. Students at Bracken engage in active learning opportunities and multidisciplinary lessons where STEM is used as a way of thinking and as a way to coherently combine content into active learning opportunities that are engaging for learners. By organizing the structural components of an exemplary STEM‐focused elementary school, we hope to deliver actionable reforms for elementary schools wanting to increase their STEM‐focused offerings.     

Categoricity in multiuniversal classes

The third author has shown that Shelah's eventual categoricity conjecture holds in universal classes: class of structures closed under isomorphisms, substructures, and unions of chains. We extend this result to the framework of multiuniversal classes. Roughly speaking, these are classes with a closure operator that is essentially algebraic closure (instead of, in the universal case, being essentially definable closure). Along the way, we prove in particular that Galois (orbital) types in multiuniversal classes are determined by their finite restrictions, generalizing a result of the second author.     

The intangible task – a revelatory case of teaching mathematical thinking in Japanese elementary schools

This paper deals with the nature of teaching mathematical thinking and presents a case study of a single Japanese lesson where the characteristics of mathematical thinking and the teaching thereof are identified in relation to multiplication. The raison d’être for this teaching is questioned and investigated by looking at how multiplication is described in the curriculum and representative textbook material. It is seen how Japanese teachers are institutionally conditioned to incorporate mathematical thinking in the context of multiplication, something which may appear in contrast to other countries. The lesson is analysed using the notion of praxeologies and didactic co-determination conceptualised in the Anthropological Theory of the Didactic.     

Nonstandard finite difference schemes for a class of generalized convection–diffusion–reaction equations

In this work, a class of nonstandard finite difference (NSFD) schemes are proposed to approximate the solutions of a class of generalized convection–diffusion–reaction equations. First, in the case of no diffusion, two exact finite difference schemes are presented using the method of characteristics. Based on these two exact schemes, a class of exact schemes are presented by introducing a parameter α. Second, since the forms of these exact schemes are so complicated that they are not convenient to use, a class of NSFD schemes are derived from the exact schemes using numerical approximations. It follows that, under certain conditions about denominator function of time‐step sizes, these NSFD schemes are elementary stable and the solutions are positive and bounded. Third, by means of the Mickens' technique of subequations, a new class of implicit NSFD schemes are constructed for the full convection–diffusion–reaction equations. It is shown that, under certain parameters set, these NSFD schemes are capable of preserving the non‐negativity and boundedness of the analytical solutions. Finally, some numerical simulations are provided to verify the validity of our analytical results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1288–1309, 2015     

一类非局部非线性扩散方程解的全局爆破

主要研究在Dirichlet边界条件或Neumann边界条件下的一类非局部非线性的扩散方程问题.在适当的假设下,证明解的存在性、唯一性、比较原则、以及解对初边值条件的连续依赖性,并就给定的初边值条件,证明解在有限时刻全局爆破.     

Automated discovery of chemically reasonable elementary reaction steps

Due to the significant human effort and chemical intuition required to locate chemical reaction pathways with quantum chemical modeling, only a small subspace of possible reactions is usually investigated for any given system. Herein, a systematic approach is proposed for locating reaction paths that bypasses the required human effort and expands the reactive search space, all while maintaining low computational cost. To achieve this, a range of intermediates are generated that represent potential single elementary steps away from a starting structure. These structures are then screened to identify those that are thermodynamically accessible, and then feasible reaction paths to the remaining structures are located. This strategy for elementary reaction path finding is independent of atomistic model whenever bond breaking and forming are properly described. The approach is demonstrated to work well for upper main group elements, but this limitation can easily be surpassed. Further extension will allow discovery of multistep reaction mechanisms in a single computation. The method is highly parallel, allowing for effective use of modern large‐scale computational clusters. © 2013 Wiley Periodicals, Inc.     

Intercalation of a Heterocyclic Ligand between Quartets in a G-Rich Tetrahelical Structure

YES G-rich oligonucleotide VK2 folds into an AGCGA-quadruplex tetrahelical structure distinct and significantly different from G-quadruplexes, even though it contains four G₃ tracts. Herein, a bis-quinolinium ligand 360A with high affinity for G-quadruplex structures and selective telomerase inhibition is shown to strongly bind to VK2. Upon binding, 360A does not induce a conformational switch from VK2 to an expected G-quadruplex. In contrast, NMR structural study revealed formation of a well-defined VK2–360A complex with a 1:1 binding stoichiometry, in which 360A intercalates between GAGA- and GCGC-quartets in the central cavity of VK2. This is the first high-resolution structure of a G-quadruplex ligand intercalating into a G-rich tetrahelical fold. This unique mode of ligand binding into tetrahelical DNA architecture offers insights into the stabilization of an AGCGA-quadruplex by a heterocyclic ligand and provides guidelines for rational design of novel VK2 binding molecules with selectivity for different DNA secondary structures.     

A Videomicroscopic Investigation of Coupled Reversible Flocculation and Coalescence at Singlet-Doublet Equilibrium in an O/W Emulsion of Low Density Contrast

Video enhanced microscopy (VEM) enables direct investigation of dilute emulsions. A practical and effective preparative technique utilizes microslides, which are flat, rectangular microcapillaries made from borosilicate glass. Experimental difficulties due to droplet sedimentation and droplet-microslide wall interaction can be drastically reduced, even eliminated, by the use of low density contrast emulsions, i.e. emulsions where the densities of the dispersed and continuous phases are not very different. The dichlorodecane (DCD)-in-water emulsion is an example of such a system. This system.can as such be used for measurement of the time of the elementary act of coalescence, calculated from the evolution in the droplet size distribution. The developing distributions can be determined through automated VEM.

In this paper we discuss the perspective for elaboration of a standard method for the determination of an averaged time for the elementary act of coalescence. The experimental basis is automated measurement of the time dependence of the droplet size distribution, as applied to dilute DCD/w emulsions at singlet-doublet equilibrium.     

Hidden information in principal component analysis of ToF‐SIMS data: On the use of correlation loadings for the identification of significant signals and structure elucidation

In this paper, an improved approach to interpret results of principal component analysis (PCA) of time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) spectra is presented. Signals are typically observed in different intensity ranges in a single ToF‐SIMS spectrum due to different sensitivity factors and surface concentrations. This can complicate the PCA interpretation, because loadings are reported to be strongly affected by these intensity changes. In contrast, it is shown here that correlation loadings are unaffected by these differences. In particular, correlation loadings were successfully used to identify signals with relatively low intensity but high significance. These signals may be overlooked when only loadings are used. This is particularly true in failure analysis, where ToF‐SIMS is used to screen for initially unknown signals that may be relevant for the characteristics/failure of a product. As a model study, the concept was applied to investigate ageing of Li‐ion batteries by ToF‐SIMS. In this data set, the significance of impurities that affect the quality of Li‐ion batteries was identified only by correlation loadings, whereas the loadings were found to overestimate the influence of other matrix signals. In addition, correlation loadings aid in the chemical identification and helped to successfully assign unknown peaks.